(* Forward lemmas with strongly rst-normalizing closures ********************)
+(* Note: this is the "big tree" theorem *)
(* Basic_2A1: uses: snv_fwd_fsb *)
-lemma cnv_fwd_fsb (a) (h): ∀G,L,T. ⦃G, L⦄ ⊢ T ![a, h] → ≥[h] 𝐒⦃G, L, T⦄.
-#a #h #G #L #T #H elim (cnv_fwd_aaa … H) -H /2 width=2 by aaa_fsb/
+lemma cnv_fwd_fsb (h) (a):
+ ∀G,L,T. ❪G,L❫ ⊢ T ![h,a] → ≥𝐒 ❪G,L,T❫.
+#h #a #G #L #T #H elim (cnv_fwd_aaa … H) -H /2 width=2 by aaa_fsb/
+qed-.
+
+(* Forward lemmas with strongly rt-normalizing terms ************************)
+
+lemma cnv_fwd_csx (h) (a):
+ ∀G,L,T. ❪G,L❫ ⊢ T ![h,a] → ❪G,L❫ ⊢ ⬈*𝐒 T.
+#h #a #G #L #T #H
+/3 width=3 by cnv_fwd_fsb, fsb_inv_csx/
qed-.
(* Inversion lemmas with proper parallel rst-computation for closures *******)
-lemma cnv_fpbg_refl_false (a) (h) (G) (L) (T):
- ⦃G, L⦄ ⊢ T ![a,h] → ⦃G, L, T⦄ >[h] ⦃G, L, T⦄ → ⊥.
+lemma cnv_fpbg_refl_false (h) (a):
+ ∀G,L,T. ❪G,L❫ ⊢ T ![h,a] → ❪G,L,T❫ > ❪G,L,T❫ → ⊥.
/3 width=7 by cnv_fwd_fsb, fsb_fpbg_refl_false/ qed-.